arXiv Machine Learning

Partially Linear Autoencoders for Manifold Learning and Dimensionality Reduction

arXiv Machine Learning

3d ago

Learning Through Energy Refinement and Manifold Projection: A Cooperative EBM-AE Framework

arXiv:2609.13917v1 Announce Type: new Abstract: Energy-Based Models (EBMs) provide a flexible framework for generative modeling by learning an energy landscape that assigns low energy values to reali...

By Ryad Zemouri

arXiv Machine Learning

Jun 17

Variational autoencoders with latent high-dimensional steady geometric flows for dynamics

arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.

By Andrew Gracyk

diffusion

arXiv Machine Learning

Jul 1

Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks

arXiv:2605. 27756v2 Announce Type: replace-cross Abstract: Linear dimensionality reduction methods such as proper orthogonal decomposition (POD) make high-dimensional data amenable to analysis by identifying the principal components, or modes, that capture the most variance, or energy, in the data and constructing a low-dimensional representation in the subspace they span.

By Tomoki Koike, Prakash Mohan, Marc T. Henry de Frahan, Elizabeth Qian, Julie Bessac

efficiency benchmarks safety

arXiv Machine Learning

Jun 4

Geometry-Preserving Encoder/Decoder in Latent Generative Models

arXiv:2501. 09876v3 Announce Type: replace-cross Abstract: Generative modeling aims to generate new data samples that resemble a given dataset.

By Wonjun Lee, Riley C. W. O'Neill, Dongmian Zou, Jeff Calder, Gilad Lerman

diffusion benchmarks

arXiv Machine Learning

Jun 17

Geodesic Calculus on Implicitly Defined Latent Manifolds

arXiv:2510. 09468v3 Announce Type: replace Abstract: Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective.

By Florine Hartwig, Josua Sassen, Juliane Braunsmann, Martin Rumpf, Benedikt Wirth

diffusion

arXiv Machine Learning

Sep 7

Nested Inductive Bias Framework for SPD Manifold Learning

The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.

By Tushar Das

rag benchmarks safety

arXiv Machine Learning

Aug 10

PCAE: Learning Ordered Representations in Latent Space for Intrinsic Dimension Estimation via Principal Component Autoencoder

arXiv:2601. 19179v2 Announce Type: replace Abstract: Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA).

By Qipeng Zhan, Zhuoping Zhou, Zexuan Wang, Li Shen

diffusion

arXiv Machine Learning

2d ago

Deep Invertible Autoencoders for Dimensionality Reduction of Dynamical Systems

arXiv:2603.13496v2 Announce Type: replace Abstract: Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of parameter-dependent high-dimensional dynamical systems...

By Nicol\`o Botteghi, Silke Glas, Christoph Brune

arXiv Machine Learning

Jul 8

Orthogonal Dendritic Intrinsic Networks: An Architecture for Significance-Ordered, Orthogonal Latent Spaces

arXiv:2607. 05653v1 Announce Type: new Abstract: Principal Component Analysis or PCA-like properties (orthogonality, variance ranking) are seldom realized in deep autoencoder architectures.

By Jeanie Schreiber, Tyrus Berry, Zeeshan Ahmed

arXiv Machine Learning

Jun 8

Constructing VAE Latent Spaces with Prescribed Topology

arXiv:2606. 07058v1 Announce Type: new Abstract: Variational autoencoders (VAEs) learn low-dimensional latent representations of high-dimensional data.

By Jilles S. van Hulst, Jakub M. Tomczak, W. P. M. H. Heemels, Duarte J. Antunes

arXiv Machine Learning

Aug 11

A solvable high-dimensional model where nonlinear autoencoders learn structure invisible to PCA while test loss misaligns with generalization

arXiv:2602. 10680v2 Announce Type: replace-cross Abstract: Many real-world datasets contain hidden structure that cannot be detected by simple linear correlations between input features.

By Vicente Conde Mendes, Lorenzo Bardone, C\'edric Koller, Jorge Medina Moreira, Vittorio Erba, Emanuele Troiani, Lenka Zdeborov\'a

arXiv Machine Learning

Aug 18

Learning symplectic model reduction based on an approximation theorem of symplectic embeddings

arXiv:2606. 04623v2 Announce Type: replace Abstract: High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics that evolve on symplectic manifolds.

By Liyi Feng, Yifa Tang, Yulin Xie, Ruili Zhang, Aiqing Zhu

rag

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